{"title":"平环面频谱的定量等分布和局部统计","authors":"Elon Lindenstrauss, Amir Mohammadi, Zhiren Wang","doi":"10.1007/s11854-023-0332-x","DOIUrl":null,"url":null,"abstract":"<p>We show that a pair correlation function for the spectrum of a flat 2-dimensional torus satisfying an explicit Diophantine condition agrees with those of a Poisson process with a polynomial error rate.</p><p>The proof is based on a quantitative equidistribution theorem and tools from geometry of numbers.</p>","PeriodicalId":502135,"journal":{"name":"Journal d'Analyse Mathématique","volume":"41 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quantitative equidistribution and the local statistics of the spectrum of a flat torus\",\"authors\":\"Elon Lindenstrauss, Amir Mohammadi, Zhiren Wang\",\"doi\":\"10.1007/s11854-023-0332-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We show that a pair correlation function for the spectrum of a flat 2-dimensional torus satisfying an explicit Diophantine condition agrees with those of a Poisson process with a polynomial error rate.</p><p>The proof is based on a quantitative equidistribution theorem and tools from geometry of numbers.</p>\",\"PeriodicalId\":502135,\"journal\":{\"name\":\"Journal d'Analyse Mathématique\",\"volume\":\"41 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-12-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal d'Analyse Mathématique\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s11854-023-0332-x\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal d'Analyse Mathématique","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s11854-023-0332-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Quantitative equidistribution and the local statistics of the spectrum of a flat torus
We show that a pair correlation function for the spectrum of a flat 2-dimensional torus satisfying an explicit Diophantine condition agrees with those of a Poisson process with a polynomial error rate.
The proof is based on a quantitative equidistribution theorem and tools from geometry of numbers.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
